Write a slope-intercept equation of the line whose graph is desrcibed,parallel to the graph of 3x+2y=5;y-intercept(0,-1)
See previous post.
To find the slope-intercept equation of a line parallel to the given line and passing through the given y-intercept, we need to determine the slope of the original line first.
The equation of the original line is 3x + 2y = 5. To convert this equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we need to solve the equation for y.
3x + 2y = 5
We isolate y by subtracting 3x from both sides:
2y = -3x + 5
Next, we divide both sides by 2 to isolate y:
y = (-3/2)x + 5/2
From this equation, we can see that the slope of the original line is -3/2.
Since we want to find a line that is parallel to the original line, the parallel line will have the same slope: -3/2.
Therefore, the slope-intercept equation of the line parallel to the graph of 3x + 2y = 5 and passing through the y-intercept (0, -1) is:
y = (-3/2)x - 1